Understanding Returns Of Leveraged And Inverse Funds

August 25, 2009


What is the likelihood that the actual beta an investor achieves over a longer holding period is close to the one-day target times the index return? Figure 6 shows that over relatively short holding periods that are longer than one day, there has been a high frequency with which leveraged and inverse funds (based on the S&P 500) approximated their daily target. Observations of long return histories for more volatile indexes show that the frequencies are lower than for the S&P 500 but still generally high. The results of our study of long-term hypothetical returns show that the longer the holding period and the more volatile the underlying benchmark, the greater the likelihood that the impact of compounding will cause the returns of a leveraged or inverse fund to deviate from the one-day target objective.



Some fund holders may have an objective of obtaining a realized beta for a longer holding period that is close to the fund’s daily target leverage ratio. The relevant question to ask is, how close? We calculate the realized betas for every holding period of two, seven and 30 days over the 50 years from 1959-2008 to determine the percentage or frequency of realized betas within selected ranges around 2 and -2. For leveraged and inverse funds that track indexes with volatility profiles similar to or lower than the S&P 500, our analysis indicates that these funds have produced realized betas reasonably close to daily target beta without any rebalancing. Figures 6 and 7 show the results in tabular and graphic form. For a hypothetical 2x S&P 500 fund, as many as 95 percent of the realized betas fell within a range of +1.5 to +2.5 (compared with a target beta of 2.0) over all possible 30-day holding periods. Even higher percentages result for two- and seven-day horizons. For a -2x fund, somewhat fewer (85 percent) realized betas fell within a -1.5 to -2.5 beta range for a 30-day holding period.



We also observed the frequency of negative betas for a 2x S&P 500 fund and of positive betas for the -2x S&P 500 daily target fund. We refer to these betas as “flipped.” Flipped returns happened rarely: less than 1 percent of the 30-day holding periods for 2x funds and about 2 percent for -2x funds.

How does the frequency of the realized betas change when the holding period is increased to six months? Figure 8 shows the realized betas for longer-term holding periods including monthly, quarterly and six-month holding periods for hypothetical 2x and -2x funds based on the S&P 500 Index. For a -2x fund, the frequency with which realized betas fall within a -1.5 to -2.5 range falls from 85 percent for 30 days to 75 percent for a quarter, and to 70 percent for six months, assuming no rebalancing. The frequency with which returns flip (realized betas are >0) for the -2x S&P 500 Index for a 180-day versus a 30-day holding period rises from 2 percent to 3.4 percent. There is a clear connection between the length of the holding period and the probability of achieving a beta close to the daily target.



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